Two-Dimensional Ferroelectric Tunnel Junction: The Case of

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Article Cite This: ACS Appl. Electron. Mater. 2019, 1, 1133−1140

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Two-Dimensional Ferroelectric Tunnel Junction: The Case of Monolayer In:SnSe/SnSe/Sb:SnSe Homostructure Xin-Wei Shen,† Yue-Wen Fang,*,†,‡ Bo-Bo Tian,† and Chun-Gang Duan*,†,§ †

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State Key Laboratory of Precision Spectroscopy and Key Laboratory of Polar Materials and Devices, Ministry of Education, Department of Optoelectronics, East China Normal University, Shanghai 200241, China ‡ Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan § Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006, China S Supporting Information *

ABSTRACT: Ferroelectric tunnel junctions, in which ferroelectric polarization and quantum tunneling are closely coupled to induce the tunneling electroresistance (TER) effect, have attracted considerable interest due to their potential in nonvolatile and low-power consumption memory devices. The ferroelectric size effect, however, has hindered ferroelectric tunnel junctions from exhibiting a robust TER effect. Here, our study proposes doping engineering in a two-dimensional in-plane ferroelectric semiconductor as an effective strategy to design a two-dimensional ferroelectric tunnel junction composed of homostructural p-type semiconductor/ferroelectric/n-type semiconductor. Because the inplane polarization persists in the monolayer ferroelectric barrier, the vertical thickness of two-dimensional ferroelectric tunnel junction can be as thin as a monolayer. We show that the monolayer In:SnSe/SnSe/Sb:SnSe junction provides an embodiment of this strategy. Combining density functional theory calculations with nonequilibrium Green’s function formalism, we investigate the electron transport properties of In:SnSe/SnSe/Sb:SnSe and reveal a giant TER effect of 1460%. The dynamical modulation of both barrier width and barrier height during the ferroelectric switching is responsible for this giant TER effect. These findings provide an important insight into the understanding of the quantum behaviors of electrons in materials at the two-dimensional limit and enable new possibilities for next-generation nonvolatile memory devices based on flexible two-dimensional lateral ferroelectric tunnel junctions. KEYWORDS: 2D materials, ferroelectrics, electron transport, TER effect, memory device

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on these conventional ferroelectric thin films cannot keep up with the ever-growing commercial needs for the ultralowpower, high-speed, and nonvolatile nanoscale memory devices. In spite of the difficulties in growing thin films of ferroelectric oxides, because of their high demand for the growth conditions,22−24 some early first-principles studies have predicted the existence of in-plane ferroelectricity in monolayer binary inorganic compounds.25,26 These works have prompted the active search for the two-dimensional (2D) ferroelectrics in both theory and experiment.27−39 Among these studies, the group IV chalcogenide semiconductors have shown to be one class of the most promising 2D ferroelectric materials. As reported in the experimental study by Chang et al., atomic thick SnTe exhibits near-room-temperature in-plane ferroelectricity, and the ferroelectricity in ultrathin SnTe films above 2 unit cells can persist above room temperature.27 A

INTRODUCTION The past decades have witnessed an explosion in the field of ferroelectric materials,1−3 headlined by the design of ferroelectric tunnel junctions (FTJs) with the aim of accelerating their commercial applications into nonvolatile information devices.4−14 FTJs are composed of two metallic electrodes separated by a thin ferroelectric barrier. The information is encoded via the nonvolatile ferroelectric polarization that can be electrically switched. Switching the polarization gives rise to a dramatic change of the tunneling electroresistance (i.e., TER effect4), making it possible to nondestructively read out the polarization state that carries information. The increasing suppression of ferroelectricity by the depolarization field as ferroelectric materials are reduced down to nanometers,15,16 or, in other words, the ferroelectric size effect,17 however, has impeded the development of nanometer-size FTJs. Although several widely studied ferroelectric oxides (e.g., BaTiO3) have been experimentally proved to show switchable polarization down to the thickness of 1−4 unit cells,18−21 the lack of stability and reproducibility at room temperature of FTJs based © 2019 American Chemical Society

Received: March 11, 2019 Accepted: June 7, 2019 Published: June 7, 2019 1133

DOI: 10.1021/acsaelm.9b00146 ACS Appl. Electron. Mater. 2019, 1, 1133−1140

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ACS Applied Electronic Materials

points along the y-axis is adopted during the calculations of transmission spectra and spatially resolved device density of states.

nonvolatile in-plane ferroelectric random access memory (FeRAM) based on 3 unit cells SnTe is designed in Chang et al.’s study to read out information nondestructively, which is more superior than conventional FeRAM where reading is destructive.27 In addition to the 2D monochalcogenide SnTe, the 2D trichalcogenide α-In2Se3, in which out-of-plane and inplane polarization are intrinsically intercorrelated, can sustain the ferroelectricity up to 700 K.37 By integration of 2D αIn2Se3 into a ferroelectric Schottky diode junction, a high current density of ∼12 A/cm2 is reported to be more than 2 times that of the conventional ferroelectric diode junctions.36 The high-quality monolayer SnTe and α-In2Se3 can be prepared by the molecular beam epitaxial technique or physical vapor deposition,27,36,40 indicating the feasibility of synthesis of 2D ferroelectric materials. These recent successes of maintaining stable electric polarization in 2D semiconductors, which are both from an experimental and from a theoretical perspective, motivate us to explore their interesting properties and potential applications in ferroelectric nonvolatile memories based on 2D-FTJs. Herein, through doping engineering in 2D semiconductors to establish electrodes (i.e., p-type and n-type semiconductors), in combination with the coupling between the robust inplane ferroelectricity and quantum tunneling in ferroelectric semiconducting barrier at the two-dimensional limit, we theoretically design a new class 2D-FTJs based on homostructure. Using a model that takes into account screening of polarization charges in electrodes, charge accumulation/ depletion at semiconductor/ferroelectric interfaces, reversible metallization of the ferroelectric barrier,41 and direct quantum tunneling across a ferroelectric barrier, we demonstrate the possibility to obtain a giant TER effect in 2D-FTJ. As an example 2D-FTJ, the In:SnSe/SnSe/Sb:SnSe homostructure is investigated by first-principles calculations with nonequilibrium Green’s function formalism. We find a giant TER effect of 1460%, which is on account of a dual modulation of both barrier width and barrier height. To our knowledge, this is the first demonstration of the 2D-FTJ based on homostructure that holds promise in future memory devices.

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RESULTS AND DISCUSSION Different from the architecture of conventional vertical FTJs built on heterostructures,51 the 2D-FTJ in our study makes the utmost of the structural features of 2D ferroelectrics. We take 2D ferroelectric group IV monochalcogenide (e.g., SnSe28 or SnTe27) as an example to elucidate our model device. As illustrated in Figure 1, a pure 2D ferroelectric monochalcoge-

Figure 1. Schematic diagram of a two-dimensional ferroelectric tunnel junction (2D-FTJ) device based on homostructure. A pure 2D monochalcogenide (MX) semiconductor with in-plane ferroelectricity serves as a tunneling barrier. The left and right electrodes are obtained by p- and n-type doping of the same MX. The inset illustrates the wave-particle duality of the quantum tunneling and the change of barrier Φ in response to the polarization reversal. Governed by quantum mechanics, the electrons tunnel across the barrier in the form of evanescent state which decays exponentially through the barrier in amplitude.

nide semiconductor is used as the ferroelectric barrier; on the other hand, its hole and electron doped forms (i.e., p-type and n-type semiconductors) work as the respective left and right electrodes concurrently. Hence, this new class of 2D-FTJ psemiconductor/ferroelectric/n-semiconductor (p-SC/FE/nSC) is architected on homostructures to avoid laminating several different materials into heterostructures as the conventional FTJs, which can be expected to reduce the difficulty in device manufacture. In Thomas−Fermi theory, the screening length of a metallic material is defined as

METHODS

The geometry optimizations and electronic structure calculations of slab models are performed within density-functional theory (DFT) by using the projector augmented wave (PAW) method, 42 as implemented in the Vienna ab initio Simulation Package (VASP).43,44 The exchange correlation functional is treated in generalized gradient approximation (GGA) with the type of Perdew−Burke−Ernzerhof (PBE).45 The kinetic-energy cutoff of 500 eV is applied to the plane wave expansion and a Γ-centered 1 × 12 × 1 k points grid is adopted for Brillouin zone sampling. All the structures are optimized until the Hellmann−Feynman forces are below 1 meV/Å, and the convergence threshold of electronic energy is 10−6 eV. A vacuum space of 15 Å is used to avoid interactions between adjacent layers. The spontaneous ferroelectric polarization (Ps) is determined by the Berry phase method.46,47 The device properties of the 2D-FTJ are calculated by using density functional theory plus nonequilibrium Green’s function formalism (DFT+NEGF approach)48,49 as implemented in the Atomistix ToolKit-Virtual NanoLab (ATK-VNL) software package.50 The double-ζ plus polarization basis set is employed, and a real-space mesh cutoff energy of 80 hartrees is used to guarantee the good convergence of the device configuration. The electron temperature is set at 300 K. The 1 × 21 × 101 k mesh is used for the self-consistent calculations to eliminate the mismatch of Fermi level between electrodes and the central region. An increased number 201 of k

δ=

1 e

ε ρ

(1)

where ε is the dielectric permittivity and ρ is the density of states at the Fermi level EF. In the homostructural 2D-FTJ displayed in Figure 1, the dielectric permittivity of left/right electrode is equivalent to that of pure 2D ferroelectric group IV monochalcogenide at saturation polarization.52 Hence, the screening lengths of the two electrodes only depend on their densities of states at the EF that can be easily controlled by doping. To introduce our model easily, we assume δ1 < δ2, in which δ1 and δ2 are the screening lengths of left and right electrodes, respectively. The model in which δ1 > δ2 can also be found in the Supporting Information. 1134

DOI: 10.1021/acsaelm.9b00146 ACS Appl. Electron. Mater. 2019, 1, 1133−1140

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Figure 2. Switching mechanisms of the 2D-FTJ p-SC/FE/n-SC. (a) The respective schematics of 2D-FTJ in P+x (left panel) and P−x (right panel) states. The black “+” and “−” symbols in the ferroelectric barrier region represent positive and negative ferroelectric bound charges, respectively. The red “+” in p-SC and blue “−” in n-SC electrodes represent hole and electrons, respectively. The “⊕” and “⊖” represent ionized donors and acceptors, respectively. (b) Distributions of charge densities. (c) Electrostatic potential energy profiles. (d) Overall potential energy profiles with corresponding band diagrams. The barrier width in either P+x or P−x state is given by the green line. The average potential barrier height is indicated by the short orange line. The Fermi level, as shown by black dashed line, is set as the reference of the barrier height.

electrostatic potential energy at p-SC/FE and FE/n-SC interfaces:

Figure 2a,b schematically depicts the charge distributions and charge density profiles in the 2D-FTJ, where d is the original width of the 2D ferroelectric barrier. When polarization is rightward (termed P+x state), negative bound charge (−Pbc) and positive ferroelectric bound charges (+Pbc) are introduced at the left edge and right edge of the ferroelectric barrier, respectively. In this case, the hole (electron) carriers in the electrode of p-SC (n-SC) become accumulated because of the spontaneous electric field at the interface (i.e., ferroelectric polarization field effect). On the contrary, the carriers in both p-SC and n-SC electrodes are depleted as the polarization is leftward (termed P−x state). To investigate the change of barrier in response to the ferroelectric switching quantitatively, we adopt a Thomas−Fermi screening mode.4 In this way, the electrostatic potentials within left and right electrodes can be written as φi = ±

ÄÅ Å ε0εiÅÅÅÅεFE ÅÇ

Pd s δi

(

δ1 ε1

+

δ2 ε2

)

ÉÑ , Ñ + d ÑÑÑÑ ÑÖ

|eφ1| ≡ |eφ(0)| < |eφ2| ≡ |eφ(d)|

(3)

We set the charge of e to “−1” in eq 3 for the simplification of model analysis; it becomes |φ1| < |φ2|. This leads to an asymmetry in the electrostatic potential energy profiles for the opposite polarization directions, which can be seen in Figure 2c. In addition to the electrostatic potential energy, we note that the tunneling electrons should also overcome electronic potential energy and potential energy barrier inside 2D ferroelectric material. As pointed out by the earlier studies4,53 the potential barriers can be assumed to be a rectangular shape of height U with respect to the Fermi level EF. Thus, the average barrier height in either P+x or P−x state can be given as ΦR = U + (φ1 − φ2)/2

i = 1 or 2

ΦL = U + (φ2 − φ1)/2 (2)

(4)

where the subscripts R and L correspond to P+x and P−x states, respectively. Setting eq 3 into eq 4 yields

where i = 1 for left electrode p-SC, i = 2 for right electrode nSC, ε0 is the permittivity of free space, εFE is the relative permittivity of the ferroelectric layer, and εi is the dielectric permittivity. The sign “+” (“−”) corresponds to the polarization pointing to (away from) the studied electrode. Using eq 2 and the assumption of δ1 < δ2, we can compare the

ΦR < ΦL

(5)

indicating the average barrier height in the P−x state is higher than that in the P+x state. The resulted barrier heights in these two states are comparatively illustrated in Figure 2d. 1135

DOI: 10.1021/acsaelm.9b00146 ACS Appl. Electron. Mater. 2019, 1, 1133−1140

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typical symmetric potential profile;59 i.e., the phase transition between its paraelectric and ferroelectric states is continuous and spontaneous below a critical temperature. By use of different valences of elements, In (Sb) is doped into monolayer SnSe to form a p-type (n-type) semiconductor. The experimental feasibility of such doped SnSe is discussed in the Supporting Information. In our study, the doped carrier concentration in In:SnSe or Sb:SnSe reaches up to 6.2 × 1020 cm−3 because the size of the unit cell In:SnSe or Sb:SnSe is composed of 4 unit cells SnSe where one Sn atom is replaced with one In or Sb atom.59 By examining the electronic structures of p-type In:SnSe and n-type Sb:SnSe,59 we found the In and Sb dopants to introduce shallow levels. Hence, the doped holes and electrons are free to move in materials. In addition, we find the density of states of In:SnSe is about 2 times that of Sb:SnSe, indicating the screening length of In:SnSe is smaller than that of Sb:SnSe according to Thomas− Fermi theory (details are provided in the Supporting Information). Therefore, In:SnSe and Sb:SnSe can act as semiconductor electrodes of a 2D-FTJ. We then set up a In:SnSe/SnSe/Sb:SnSe homostructure as an implementation of p-SC/FE/n-SC 2D-FTJ. In this In:SnSe/SnSe/Sb:SnSe homostructure, the region of ferroelectric SnSe is a stacking of 18 unit cells along the [100] direction (∼8 nm), and In:SnSe (Sb:SnSe) plays as the p-type (n-type) semiconductor electrode. The optimized atomic structures of In:SnSe/SnSe/ Sb:SnSe homostructure in the P+x and P−x states are displayed in Figure 3a. In addition to the robust ferroelectric displacements in the barrier region, we find the polar displacements

Besides, it follows from Figure 2d that the effective barrier width can also be changed by the polarization switching. As pointed out by some recent experimental and theoretical studies,54−57 off-center displacements and metallic conductivity can coexist in doped ferroelectrics. In our 2D-FTJ model, we consider such a condition where the introduced dopants in the electrodes will not eliminate the polar distortions completely; i.e., the electrodes enter polar metallic states. In addition, we note that charge leakage can be induced at the interface when a polar metallic material is interfaced with a ferroelectric material.41,58 For the P+x state of 2D-FTJ, carriers are accumulated at the p-SC/FE and n-SC/FE interfaces. This leads to the enhancement of the charge leakage, and therefore the regions of ferroelectric barrier near the two interfaces may become conductive, resulting in reduction of the effective tunneling width. We refer to this decreased tunneling width as d1, which is smaller than the original width d of the ferroelectric barrier, as can be seen from the left panel of Figure 2d. By contrast, carriers are depleted at the two interfaces in the P−x state. The majority carriers will be partially canceled out near the semiconductor/ferroelectric interfaces, only leaving the immobile ionized acceptors and donors,53 as shown in the right panel of Figure 2a. Under this condition, charge leakage of the P−x state is weaker than the P+x state. As a result, some ferroelectric barrier regions near interfaces will transform back into the insulating state, and the band alignment in the P−x state is also changed with respect to the P+x state. If the charge leakage is sufficiently weak, all the ferroelectric barrier regions and even partial regions in the electrodes may become insulating.41 In this case, the effective barrier width is increased to d2, which is larger than the effective barrier width d1 of the P+x state. The modulation of effective barrier width is also known as the “reversible metallization of the barrier” as reported by Liu et al.41 It is due to the ferroelectric dual modulation of both barrier width and barrier height in 2D-FTJ; the tunneling electrons in the P−x state have to overcome additional barrier height and barrier width. Because the tunneling conductance is determined by the barrier height and barrier width,4 the conductance of the P+x state will be dramatically enhanced compared to the P−x state. The higher conductance state is conventionally termed the “ON” state, with a comparison of the lower conductance state termed the “OFF” state, as displayed in Figure 2d. We note that in conventional FTJs like Metal-1/ferroelectric/Metal-2 heterostructures6 only barrier height is generally modified by polarization switching. Therefore, the 2D-FTJs in our study can be expected to realize the enhanced TER effect. To realize the functional 2D-FTJ p-SC/FE/n-SC, we turn to study real materials. SnSe is a 2D monochalcogenide with robust in-plane ferroelectric polarization above room temperature, as pointed out by ref 28. The crystal structure of monolayer SnSe is explicitly provided in the Supporting Information. In the xy-plane, the ferroelectric polarization along the x- and y-axis are equivalent due to the symmetry,59 and we will only discuss the case along x-direction throughout the study. Using the Berry phase approach,46,47 we have revisited its polarization in the monolayer limit and found it is ∼1.82 × 10−10 C/m, in agreement with a previous study.28 In the Supporting Information, we also revisit the double-well potential energy profile of monolayer SnSe and its lattice dynamics properties. As many other ferroelectric materials like bulk BaTiO3 and PbTiO3,60 monolayer SnSe also features a

Figure 3. (a) Calculated atomic structure and the schematic diagram (shaded regions) of 2D-FTJ In:SnSe/SnSe/Sb:SnSe. The red and blue arrows indicate P+x and P−x, respectively. Only a few unit cells are shown for illustrating the ferroelectric barrier region and electrode regions because of the page width limitations. The lengths along the x-axis in P+x and P−x states are both 114 Å. (b) Calculated asymmetric potential energy profile as a function of ferroelectric distortions in the 2D-FTJ In:SnSe/SnSe/Sb:SnSe. The ferroelectric displacements λ along [100] directions are normalized so that λ = +1 and −1 correspond to the P+x and P−x states, respectively. The energy is summed up to all the atoms in the structure. The energy of the P−x state is set as the reference. 1136

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Figure 4. (a) Device configurations in the DFT+NEGF calculations for P+x and P−x states. (b) k∥-resolved transmissions in 2D Brillouin zone at the Fermi energy through the 2D-FTJ In:SnSe/SnSe/Sb:SnSe for P+x and P−x states. Polarization directions are shown by arrows. The k∥-resolved transmissions for P+x and P−x states use the same scale as given by the color bar.

remain in the In:SnSe and Sb:SnSe regions. In contrast to the conventional Metal-1/ferroelectric/Metal-2 FTJ6 or all-oxide FTJ61 in which lattice mismatch is inevitably generated by the electrodes and ferroelectrics due to their unmatched lattice constants, our In:SnSe/SnSe/Sb:SnSe homostructure completely eliminates the lattice constant mismatch and will not introduce abrupt structure distortions at the ferroelectric/ electrode interfaces. In addition, the ferroelectric polarization of monolayer SnSe in this 2D-FTJ is spontaneous, which avoids using sophisticated chemical methods29,62 to maintain stable and switchable 2D ferroelectricity. The stability and robustness of in-plane ferroelectricity in a 2D ferroelectric barrier sandwiched between two doped electrodes lies at the heart of the 2D-FTJ device. To verify the in-plane ferroelectricity of monolayer SnSe barrier survives in the monolayer In:SnSe/SnSe/Sb:SnSe homostructure, we compute the total energy of the homostructure as a function of normalized polar displacements λ. As shown in Figure 3b, a double-well potential profile is observed, indicating the stability of ferroelectricity in the monolayer SnSe. This can be ascribed to the small depolarization field of 6.5 × 106 V/m in SnSe barrier, which can be well screened by the left/right electrodes (see the Supporting Information for more details). Different from a free-standing SnSe monolayer with a symmetric potential profile,59 the monolayer In:SnSe/SnSe/Sb:SnSe homostructure displays an asymmetric potential profile: (1) the energy minima at λ = −1 (i.e., P−x state) and λ = 1 (P+x state) are inequivalent with energy difference of 161.25 meV/ homostructure; (2) the energy maximum corresponding to a paraelectric phase is approximately located at λ = 0.2, which slightly deviates from λ = 0. This asymmetry is a consequence of the symmetry breaking introduced by the two different dopants in the two electrodes. The asymmetry can also be observed from the polar displacements profile in the Supporting Information. These results indicate the barriers at the two interfaces are also asymmetric and will be responsible for the TER effect.63

To evaluate the performance of 2D-FTJ In:SnSe/SnSe/ Sb:SnSe, density functional theory plus nonequilibrium Green’s function formalism is used to study the electrical conductance and TER effect. The device configurations for P+x and P−x states are explicitly shown in Figure 4a. The left/right extension layer (buffer layer) is as wide as around 35 Å, which is confirmed to be large enough to screen the electrostatic potential.59 In our calculations, the transmission coefficients and reflection matrices are determined by matching the wave functions of the scattering region with linear combinations of propagating Bloch states in the electrodes. Because the electronic states at the EF dominate the transport properties, the zero-bias electrical conductance within the Landauer− Büttiker formula64 can be evaluated as G = G0 ∑ T (E F , k ) (6)

k 2

where G0 = 2e /h is the conductance quantum, e is the electron charge, h is the Planck’s constant, and T(EF,k∥) is the transmission coefficient at the Fermi energy for a given Bloch wave vector k∥ = (kx, ky) in the 2D Brillouin zone. By integrating the transmission probability for states at the Fermi energy over the 2D Brillouin zone, we can calculate the total conductance (G). In the P+x state, GR = 1.003 × 10−9 S; by contrast, in the P−x state, GL = 6.435 × 10−11 S. Following the conventional definition in previous study,61 the TER ratio in our study is defined as TER =

GR − GL GL

(7)

As a result, the reversal of ferroelectric polarization in the 2DFTJ In:SnSe/SnSe/Sb:SnSe leads to a significantly enhanced TER effect at zero bias, which is approximately about 1460%. This TER effect is about 1 order larger than those in conventional all-oxide FTJs such as LaNiO3 /BaTiO 3/ LaNiO363 and SrRuO3/BaTiO3/SrRuO361 at zero bias. Note that the migrations of electrons or holes near the semi1137

DOI: 10.1021/acsaelm.9b00146 ACS Appl. Electron. Mater. 2019, 1, 1133−1140

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Figure 5. Device density of states (DDOS) of the 2D-FTJ In:SnSe/SnSe/Sb:SnSe device projected onto its x-axis. (a) P+x state. (b) P−x state. The abscissa is the Cartesian coordinate of central region along the x-axis. The color bar on the right indicates the DOS amplitude. Eci and Evi are the conduction band minimum and valence band maximum of the electrodes, respectively. The Fermi level is set to zero, which is shown by the white dashed line. The interface of semiconductor/ferroelectric is initially set to be located around 35 and 114 Å. The black arrow indicates the interface between 2D ferroelectric SnSe and electrode In:SnSe (Sb:SnSe). The red rectangle represents the region of effective ferroelectric tunneling barrier, and the red dashed lines are used to guide the evolution of the valence band maximum along the x-axis. The green arrow indicates the width of the tunneling barrier. The black regions in the tunneling regions indicate the band gap of the ferroelectric barrier.

that the band diagrams calculated by the DFT+NEGF approach are qualitatively consistent with those obtained in our model in Figure 2. In particular, the barrier width in the P−x state is indeed increased compared to the P+x state because of the interfacial metallization of the edge regions in ferroelectric barrier controlled by the ferroelectric switching. In Figure 5, we have used red solid rectangles to highlight the effective tunneling regions, in which the evolution of the valence band maximum along the x-axis is guided by the red dashed line. The built-in electric field caused by the work function step can be clearly observed through the tilting of bands in SnSe.66 When the ferroelectric polarization is pointing to the right (i.e., P+x state), the depolarizing field is parallel to the built-in electric field, and hence the band edges in SnSe are tilted. On the other hand, the bands of SnSe become slightly flat since the depolarization field is antiparallel to the built-in field in the P−x state. More details about the reversible metallization of the monolayer SnSe barrier can be found in the layer-resolved density of states provided in the Supporting Information. Therefore, in addition to the raised barrier height as polarization is flipped from the P+x to P−x state, the barrier width is also increased. This makes the electron tunneling much easier in the P+x state than in the P−x state, which accounts for the observed giant TER effect.

conductor surfaces are nearly ignored during the transport calculations in which only electron cloud diffusion is taken into account, making the change of barrier width underestimated by ferroelectric polarization reversal. Hence, the actual TER effect in experiment should be even higher than the theoretical value.53 In addition, although the band gap of the semiconductor is usually underestimated in DFT calculations, we find the correction of band gap of ferroelectric barrier does not affect the TER effect of the studied 2D-FTJ significantly,59 which is similar to the conventional FTJs.65 To understand the large change in the conductance ratio during the polarization reversal, the k∥-resolved transmissions at EF are shown in Figure 4b. In the P+x state, the transmission coming from the two blue stripe regions (around ky = +0.42/− 0.42) of the 2D Brillouin zone are largest, indicating the feature of resonant tunneling. We find the transmission eigenstates around this region show much smaller decay rate than those around Γ point, which is responsible for the significant transmission. The discussions of transmission eigenstates are available in the Supporting Information. Compared to the P+x state, the transmission in the P−x state is largely reduced, leading to lower conductance than the P+x state. This explains the observed giant TER effect in the monolayer In:SnSe/SnSe/Sb:SnSe homostructure. Finally, we compare the effective barriers for the two polarization states in the 2D-FTJ In:SnSe/SnSe/Sb:SnSe. As mentioned above, the combination of DFT-calculated density of states and Thomas−Fermi theory indicates the screening length of left electrode In:SnSe is smaller than the right electrode Sb:SnSe; this indicates the assumption that δ1 < δ2 in the model of Figure 2 is indeed true in our studied case. We can then get ΦR < ΦL through eqs 3 and 4; i.e., the barrier height for the P+x state is smaller than that for the P−x state. To understand the change of barrier width, we study the electronic structure across the 2D-FTJ In:SnSe/SnSe/Sb:SnSe device by carrying out the analysis of real-space device DOS (DDOS) projected onto the device x-axis. The corresponding results for the two polarization states are displayed in Figure 5. We find

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CONCLUSIONS In summary, we have proposed a method to design twodimensional ferroelectric tunnel junction based on planar ptype semiconductor/ferroelectric/n-type semiconductor homostructure via the doping engineering in a two-dimensional ferroelectric semiconductor with in-plane electric polarization. Combining density functional theory calculations with nonequilibrium Green’s function formalism, a giant TER effect of 1460% is observed in our newly designed 2D-FTJ In:SnSe/ SnSe/Sb:SnSe homostructure, which is comparable to that of conventional all-oxide FTJs. The tunable tunneling barrier width that is generally absent in conventional FTJs, as well as the tunneling barrier height, is responsible for the enhanced 1138

DOI: 10.1021/acsaelm.9b00146 ACS Appl. Electron. Mater. 2019, 1, 1133−1140

Article

ACS Applied Electronic Materials

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TER effect. The dynamical modulation of barrier width stems from the depletion/accumulation of majority carriers near the semiconductor surface in response to the reversal of ferroelectricity. SnSe is thought to be the most flexible in known 2D atomic materials;67 hence, monolayer In:SnSe/ SnSe/Sb:SnSe homostructures can be promising memory blocks in the wearable devices and artificial synapses, which has larger advantages over the conventional FTJs. The proposed strategy in our study is applicable to design novel 2D-FTJs using other 2D ferroelectric materials. We hope this work will stimulate the experimental endeavors of fabricating 2D-FTJs with a giant TER effect to accelerate their commercial applications into ultralow-power, high-speed, and nonvolatile nanoscale memory devices.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsaelm.9b00146.

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Overall potential energy profile if δ1 > δ2; in-plane ferroelectricity in monolayer SnSe; carrier concentration in doped SnSe; phonon dispersions; dopants with shallow levels; screening lengths in electrodes; experimental feasibility; depolarization field; polar displacements profile; layer-resolved density of states; transmission eigenstate; width of extension layer; Hubbard U effect (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Yue-Wen Fang: 0000-0003-3674-7352 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key R&D Program of China (2017YFA0303403), the National Natural Science Foundation of China (Grants 11774092 and 51572085), and the Shanghai Science and Technology Innovation Action Plan (No. 17JC1402500). Computations were performed at the ECNU computing center.

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